830 research outputs found
(2+1)-Gravity Solutions with Spinning Particles
We derive, in 2+1 dimensions, classical solutions for metric and motion of
two or more spinning particles, in the conformal Coulomb gauge introduced
previously. The solutions are exact in the -body static case, and are
perturbative in the particles' velocities in the dynamic two-body case. A
natural boundary for the existence of our gauge choice is provided by some
``CTC horizons'' encircling the particles, within which closed timelike curves
occur.Comment: 30 pages, LaTeX, no figure
The 2+1 Kepler Problem and Its Quantization
We study a system of two pointlike particles coupled to three dimensional
Einstein gravity. The reduced phase space can be considered as a deformed
version of the phase space of two special-relativistic point particles in the
centre of mass frame. When the system is quantized, we find some possibly
general effects of quantum gravity, such as a minimal distances and a foaminess
of the spacetime at the order of the Planck length. We also obtain a
quantization of geometry, which restricts the possible asymptotic geometries of
the universe.Comment: 59 pages, LaTeX2e, 9 eps figure
Pauli-Lubanski scalar in the Polygon Approach to 2+1-Dimensional Gravity
In this paper we derive an expression for the conserved Pauli-Lubanski scalar
in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point
particles. We find that it is represented by an extra spatial shift in
addition to the usual identification rule (being a rotation over the cut). For
two particles this invariant is expressed in terms of 't Hooft's phase-space
variables and we check its classical limit.Comment: Some errors are corrected and a new introduction and discussion are
added. 6 pages Latex, 4 eps-figure
Self-organized criticality induced by quenched disorder: experiments on flux avalanches in NbH films
We present an experimental study of the influence of quenched disorder on the
distribution of flux avalanches in type-II superconductors. In the presence of
much quenched disorder, the avalanche sizes are power-law distributed and show
finite size scaling, as expected from self-organized criticality (SOC).
Furthermore, the shape of the avalanches is observed to be fractal. In the
absence of quenched disorder, a preferred size of avalanches is observed and
avalanches are smooth. These observations indicate that a certain minimum
amount of disorder is necessary for SOC behavior. We relate these findings to
the appearance or non-appearance of SOC in other experimental systems,
particularly piles of sand.Comment: 4 pages, 4 figure
Mechanical Instabilities of Biological Tubes
We study theoretically the shapes of biological tubes affected by various
pathologies. When epithelial cells grow at an uncontrolled rate, the negative
tension produced by their division provokes a buckling instability. Several
shapes are investigated : varicose, enlarged, sinusoidal or sausage-like, all
of which are found in pathologies of tracheal, renal tubes or arteries. The
final shape depends crucially on the mechanical parameters of the tissues :
Young modulus, wall-to-lumen ratio, homeostatic pressure. We argue that since
tissues must be in quasistatic mechanical equilibrium, abnormal shapes convey
information as to what causes the pathology. We calculate a phase diagram of
tubular instabilities which could be a helpful guide for investigating the
underlying genetic regulation
Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
By investigating the canonical commutation rules for gravitating quantized
particles in a 2+1 dimensional world it is found that these particles live on a
space-time lattice. The space-time lattice points can be characterized by three
integers. Various representations are possible, the details depending on the
topology chosen for energy-momentum space. We find that an
topology yields a physically most interesting lattice within which first
quantization of Dirac particles is possible. An topology also gives a
lattice, but does not allow first quantized particles.Comment: 23 pages Plain TeX, 3 Figure
Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in
the maximally slicing gauge has hamiltonian form. This is proved directly for
the two body problem and for the three body problem by using the Garnier
equations for isomonodromic transformations. For a number of particles greater
than three the existence of the hamiltonian is shown to be a consequence of a
conjecture by Polyakov which connects the auxiliary parameters of the fuchsian
differential equation which solves the SU(1,1) Riemann-Hilbert problem, to the
Liouville action of the conformal factor which describes the space-metric. We
give the exact diffeomorphism which transforms the expression of the spinning
cone geometry in the Deser, Jackiw, 't Hooft gauge to the maximally slicing
gauge. It is explicitly shown that the boundary term in the action, written in
hamiltonian form gives the hamiltonian for the reduced particle dynamics. The
quantum mechanical translation of the two particle hamiltonian gives rise to
the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit
is given by the total energy of the system irrespective of the masses of the
particles thus proving at the quantum level a conjecture by 't Hooft on the two
particle dynamics. The quantum mechanical Green's function for the two body
problem is given.Comment: 34 pages LaTe
(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame
We formulate and analyze the Hamiltonian dynamics of a pair of massive
spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the
system to a conical infinity, isometric to the infinity generated by a single
massive but possibly spinning particle. The reduced phase space \Gamma_{red}
has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the
phase space of a Newtonian two-body system in the centre-of-mass frame, and we
find on \Gamma_{red} a canonical chart that makes this analogue explicit and
reduces to the Newtonian chart in the appropriate limit. Prospects for
quantization are commented on.Comment: 38 pages, REVTeX v3.1 with amsfonts and epsf, 12 eps figures. (v2:
Presentational improvement, references added, typos corrected.
Hamiltonian structure of 2+1 dimensional gravity
A summary is given of some results and perspectives of the hamiltonian ADM
approach to 2+1 dimensional gravity. After recalling the classical results for
closed universes in absence of matter we go over the the case in which matter
is present in the form of point spinless particles. Here the maximally slicing
gauge proves most effective by relating 2+1 dimensional gravity to the Riemann-
Hilbert problem. It is possible to solve the gravitational field in terms of
the particle degrees of freedom thus reaching a reduced dynamics which involves
only the particle positions and momenta. Such a dynamics is proven to be
hamiltonian and the hamiltonian is given by the boundary term in the
gravitational action. As an illustration the two body hamiltonian is used to
provide the canonical quantization of the two particle system.Comment: 13 pages,2 figures,latex, Plenary talk at SIGRAV2000 Conferenc
Efficient Attack Graph Analysis through Approximate Inference
Attack graphs provide compact representations of the attack paths that an
attacker can follow to compromise network resources by analysing network
vulnerabilities and topology. These representations are a powerful tool for
security risk assessment. Bayesian inference on attack graphs enables the
estimation of the risk of compromise to the system's components given their
vulnerabilities and interconnections, and accounts for multi-step attacks
spreading through the system. Whilst static analysis considers the risk posture
at rest, dynamic analysis also accounts for evidence of compromise, e.g. from
SIEM software or forensic investigation. However, in this context, exact
Bayesian inference techniques do not scale well. In this paper we show how
Loopy Belief Propagation - an approximate inference technique - can be applied
to attack graphs, and that it scales linearly in the number of nodes for both
static and dynamic analysis, making such analyses viable for larger networks.
We experiment with different topologies and network clustering on synthetic
Bayesian attack graphs with thousands of nodes to show that the algorithm's
accuracy is acceptable and converge to a stable solution. We compare sequential
and parallel versions of Loopy Belief Propagation with exact inference
techniques for both static and dynamic analysis, showing the advantages of
approximate inference techniques to scale to larger attack graphs.Comment: 30 pages, 14 figure
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